Performance Of Differential Evolution Algorithm Research Articles

Performance of Differential Evolution Algorithms for Indoor Area Positioning in Wireless Sensor Networks

In positioning systems in wireless sensor networks, the accuracy of localization is often affected by signal distortion or attenuation caused by environmental factors, especially in indoor environments. Although using a combination of K-Nearest Neighbor (KNN) algorithm and fingerprinting matching can reduce positioning errors due to poor signal quality, the improvement in accuracy by increasing the number of reference points and K values is not significant. This paper proposes a Differential Evolution-based KNN (DE-KNN) method to overcome the performance limitations of the KNN algorithm and enhance indoor area positioning accuracy in WSNs. The DE-KNN method aims to improve the accuracy and stability of indoor positioning in wireless sensor networks. According to the simulation results, in a simple indoor environment with four reference points, when the sensors are deployed in both fixed and random arrangements, the positioning accuracy was improved by 29.09% and 30.20%, respectively, compared to using the KNN algorithm alone. In a complex indoor environment with four reference points, the positioning accuracy was increased by 32.24% and 33.72%, respectively. When the number of reference points increased to five, in a simple environment, the accuracy improvement for both fixed and random deployment was 20.70% and 26.01%, respectively. In a complex environment, the accuracy improvement was 23.88% and 27.99% for fixed and random deployment, respectively.

A Metaheuristic Approach to Parameter Estimation of a Flexible Parametric Mixture Cure Rate Model with Interval-Censored Data

A flexible parametric mixture cure model, called bi-lognormal cure rate model or simply BLN model, is defined and studied. The BLN model can be effectively used to analyze survival dataset in the presence of long-term survivors, especially when the dataset presents the underlying phenomenon of latent competing risks or when there is evidence that a bimodal hazard function is appropriated to described it, which are advantages over other cure rate models found in the literature. We discuss the maximum likelihood estimation for the model parameters considering interval-censored data through the differential evolution algorithm that is a nature-inspired computing metaheuristic used for global optimization of functions defined in multidimensional spaces. This approach is also used because the likelihood function of the model is multimodal and the direct application of gradient methods in this case is not ideal, since such methods are local search methods with a high chance of getting stuck at a local maximum when the starting point is chosen outside the basin of attraction of a global maximum. In addition, a simulation study was implemented to compare the performance of differential evolution algorithm with the performance of the Newton-Raphson algorithm in terms of bias, root mean square error, and the coverage probability of the asymptotic confidence intervals for the parameters. Finally, an application of the BLN model to real data is presented to illustrate that it can provide a better fit than other mixture cure rate models.

Improved multi-objective differential evolution algorithm based on a decomposition strategy for multi-objective optimization problems

Many real-world engineering problems need to balance different objectives and can be formatted as multi-objective optimization problem. An effective multi-objective algorithm can achieve a set of optimal solutions that can make a tradeoff between different objectives, which is valuable to further explore and design. In this paper, an improved multi-objective differential evolution algorithm (MOEA/D/DEM) based on a decomposition strategy is proposed to improve the performance of differential evolution algorithm for practical multi-objective nutrition decision problems. Firstly, considering the neighborhood characteristic, a neighbor intimacy factor is designed in the search process for enhancing the diversity of the population, then a new Gaussian mutation strategy with variable step size is proposed to reduce the probability of escaping local optimum area and improve the local search ability. Finally, the proposed algorithm is tested by classic test problems (DTLZ1-7 and WFG1-9) and applied to the multi-objective nutrition decision problems, compared to the other reported multi-objective algorithms, the proposed algorithm has a better search capability and obtained competitive results.

Probabilistic Analysis of Search Performance of Differential Evolution Algorithm in Low-Dimensional Case

In this paper, a method of establishing and analyzing the probability model of its mutation and crossoperation process for differential evolution (DE) algorithm is proposed; especially, the escape ability and further optimization ability of individuals trapped in the local optimal neighborhood are deduced in detail, and the characteristic curves of the influence of key parameters such as population size, scaling factor, and crossfactor on the search performance of the algorithm are obtained. It provides a theoretical reference for the application of the algorithm.

Enhancing differential evolution with a target vector replacement strategy

Individuals find it difficult to avoid stagnation in the iterative process of the differential evolution (DE) algorithm, and the stagnant individuals have restricted improvement in the population, which will have a negative effect on its performance. This research put forward a target vector replacement strategy (TVRS) for reducing the impact of stagnant individuals on the DE algorithm's performance. For stagnant target vectors, while executing mutation operation and crossover operation, TVRS selects non-stagnant individuals in the population to replace the stagnant target vectors with a specific probability. Because improving stagnant individuals are difficult, TVRS provides more opportunities for improvement to those who are not stagnant, while the opportunities for stagnant individuals to be improved are decreased. For assessing the efficiency of TVRS, TVRS was implemented to six DE algorithms and compared to their original algorithms. Judging from the performance outcomes of TVRS in the CEC 2014 benchmark test set, TVRS can greatly increase the DE algorithm's performance. This study will show the evolutionary opportunity that is obtained by an individual should be related to the individual state. Adjusting the individual evolutionary opportunity based on the individual state is helpful for improving the stagnation problem of the differential evolution algorithm. This study will provide a new way for improving the stagnation problem of the differential evolution algorithm and other evolutionary algorithms.

An adaptive mutation strategy for differential evolution algorithm based on particle swarm optimization

Differential evolution (DE) algorithm is a very effective algorithm used for solving wide range of optimization problems. However, the performance of DE is dependent on the control parameters and to choose the right parameter value and tuning of these parameters is a challenging task. Therefore, a novel variant of differential evolution algorithm based on particle swarm optimization (DEPSO) is proposed to improve the overall performance of Differential evolution algorithm. In our proposed approach, we are using DE mutation strategy during the initial phase of evolution and therefore enlarge its search space possibly to the extent that helps in finding more encouraging results and thus avoid premature convergence. During the subsequent phase of evolution process, this value of sigmoid function reduces with the increase of number of iterations. In this scenario, there is a greater probability of operating PSO mutation strategy and thus this sigmoid function helps in improving the precision and convergence speed. The Performance of our proposed algorithm is tested with 10 benchmark test functions on 50 and 25 dimensions set, also tested with 11 test functions on 30- and 100-dimension test functions. We have also tested our proposed algorithm with 8 test functions on high dimension set as 500- and 1000-dimensions. The performance comparison shows that our proposed variant is giving significant improvement in convergence speed and thus avoiding premature convergence. Average performance of DEPSO is better than classical DE, PSO and other algorithms in comparison.

Di-DE: Depth Information-Based Differential Evolution With Adaptive Parameter Control for Numerical Optimization

Differential Evolution (DE) is a simple and effective stochastic algorithm for optimization problems, and it became much more popular in recent year because of its easy-implementation and excellent performance. Nevertheless, the performance of DE algorithm is greatly affected by the trial vector generation strategy including mutation strategy and parameter control, both of which still exist some weaknesses, e.g. the premature convergence to some local optima of a mutation strategy and the misleading interaction among control parameters. Therefore in this paper, a novel Di-DE algorithm is proposed to tackle these weaknesses. A depth information based external archive was advanced in our novel mutation strategy, which can get a better perception of the landscape of objective in an optimization. Moreover, a novel grouping strategy was also employed in Di-DE and parameters were updated separately so as to avoid the misleading among parameters. Moreover, a cooperative strategy for information interchange was also advanced aiming at improving the efficiency of the exploration behavior. By absorbing these advancements, the novel Di-DE algorithm can secure better performance in comparison with other famous optimization algorithms. The algorithm validation was conducted on CEC2013 and CEC2017 test suites, and the results revealed the competitiveness of our Di-DE algorithm in comparison with those famous optimization algorithms including Particle Swarm Optimization (PSO) variants, QUasi-Affine TRansformation Evolution (QUATRE) variants and Differential Evolution (DE) variants.

Optimization of Wireless Sensor Networks Based on Differential Evolution Algorithm

To study the optimization problem of wireless sensor network (WSN) based on differential evolution, the single objective differential evolution algorithm is applied and combined with the advantages and disadvantages crossover strategy. Firstly, the path optimization problem in WSN is analyzed, and the optimization model is established. Then, the differential evolution algorithm is used as the search tool to solve the minimum energy consumption in the path optimization model, that is, the optimal path problem. Finally, the comparison experiment is carried out on the classical algorithm genetic algorithm (GA), particle swarm optimization (PSO) and standard differential evolution (DE) algorithm. The results show that the performance of differential evolution algorithm based on crossover strategy is superior to or not worse than that of several contrast algorithms. It can be seen that the differential evolution algorithm based on advantage and disadvantage crossover strategy has good effectiveness.

Optimization of Wave Energy Converter Arrays by an Improved Differential Evolution Algorithm

Since different incident waves will cause the same array to perform differently with respect to the wave energy converter (WEC), the parameters of the incident wave, including the incident angle and the incident wave number, are taken into account for optimizing the wave energy converter array. Then, the differential evolution (DE) algorithm, which has the advantages of simple operation procedures and a strong global search ability, is used to optimize the wave energy converter array. However, the traditional differential evolution algorithm cannot satisfy the convergence precision and speed simultaneously. In order to make the optimization results more accurate, the concept of an adaptive mutation operator is presented to improve the performance of differential evolution algorithm. It gives the improved algorithm a faster convergence and a higher precision ability. The three-float, five-float, and eight-float arrays were optimized, respectively. It can be concluded that the larger the size of the array is, the greater the interaction between the floats is. Hence, a higher efficiency of wave energy extraction for wave energy converter arrays is achieved by the layout optimization of the array of wave energy converters. The results also show that the optimal layout of the array system is inhomogeneously distributed and that the improved DE algorithm used on array optimization is superior to the traditional DE algorithm.

Optimization of Model Reference Adaptive Controller for the Inverted Pendulum System Using CCPSO and DE Algorithms

The main aim of this paper is to propose two variants of bio-inspired algorithm, Constriction Coefficient Particle Swarm Optimization (CCPSO) and Differential Evolution (DE), which determine optimal parameters of Proportional-Integral-Derivative (PID) controller. To achieve this purpose, the PID controller has been plugged to the Model Reference Adaptive Controller (MRAC) that balances Inverted Pendulum (IP) with nonlinear characteristic in vertical-upright position. For comparison purpose, efficiency of these intelligent approaches to adjust MRAC parameters has been evaluated in terms of time response performance. Finally, the overall simulation results demonstrate that both the algorithms yield acceptable response in controlling the nonlinear model of IP system. However, the performance of DE algorithm is better than CCPSO in terms of transient response characteristics.

An Improved Binary Differential Evolution Algorithm for Feature Selection in Molecular Signatures.

The discovery of biomarkers from high-dimensional data is a very challenging task in cancer diagnoses. On the one hand, biomarker discovery is the so-called high-dimensional small-sample problem. On the other hand, these data are redundant and noisy. In recent years, biomarker discovery from high-throughput biological data has become an increasingly important emerging topic in the field of bioinformatics. In this study, we propose a binary differential evolution algorithm for feature selection. Firstly, we suggest using a two-stage approach, where three filter methods including the Fisher score, T-statistics, and Information gain are used to generate the feature pool for input to differential evolution (DE). Secondly, in order to improve the performance of differential evolution algorithm for feature selection, a new variant of binary DE called BDE is proposed. Three optimization strategies are incorporated into the BDE. The first strategy is the heuristic method in initial stage, the second one is the self-adaptive parameter control, and the third one is the minimum change value to improve the exploration behaviour thus enhance the diversity. Finally, Support vector machine (SVM) is used as the classifier in 10 fold cross-validation method. The experimental results of our proposed algorithm on some benchmark datasets demonstrate the effectiveness of our algorithm. In addition, the BDE forged in this study will be of great potential in feature selection problems.

Research on solving the optimal sizing and siting of distributed generation

In this paper, a distributed network planning model is proposed with the goal of minimizing the sum of distributed power investment cost, network loss and interruption cost. In order to compare the performance of differential evolution algorithm (DE) and genetic algorithm (GA) in solving the optimal sizing and siting of distributed generation in distribution networks, the two algorithms were adopted to optimize the capacities and positions of DGs. Through analysis on a 10-bus test system, the study results show that the proposed model and algorithm can get reasonable planning scheme. And in solving simple optimization problems, both GA and DE Algorithms can get good results, but compare to DE, GA is of slow convergence speed and the convergence process is not quite stable.

Fitness Proportionate Random Vector Selection based DE Algorithm (FPRVDE)

Differential Evolution (DE) is a simple, powerful and easy to use global optimization algorithm. DE has been studied in detail by many researchers in the past years. In DE algorithm trial vector generation strategies have a significant influence on its performance. This research studies that whether performance of DE algorithm can be improved by incorporating selection advancement in effective trial vector generation strategies. A novel advancement in DE trial vector generation strategies is proposed in this research to speeds up the convergence speed of DE algorithm. The proposed fitness proportion based random vector selection DE (FPRVDE) is based on the proportion of individual fitness mechanism. FPRVDE reduces the role of poor performing individuals to enhance it performance capability of DE algorithm. To form a trial vector using FPRVDE, individual based on the proportion of their fitness are selected. FPRVDE mechanism is applied to most commonly used set of DE variants. A comprehensive set of multidimensional function optimization problems is used to access the performance of FPRVDE. Experimental result shows that proposed approach accelerates DE algorithm.

Parameter identification of PEMFC model based on hybrid adaptive differential evolution algorithm

In this paper, a HADE (hybrid adaptive differential evolution) algorithm is proposed for the identification problem of PEMFC (proton exchange membrane fuel cell). Inspired by biological genetic strategy, a novel adaptive scaling factor and a dynamic crossover probability are presented to improve the adaptive and dynamic performance of differential evolution algorithm. Moreover, two kinds of neighborhood search operations based on the bee colony foraging mechanism are introduced for enhancing local search efficiency. Through testing the benchmark functions, the proposed algorithm exhibits better performance in convergent accuracy and speed. Finally, the HADE algorithm is applied to identify the nonlinear parameters of PEMFC stack model. Through experimental comparison with other identified methods, the PEMFC model based on the HADE algorithm shows better performance.

Quantum Inspired Differential Evolution Algorithm

To enhance the optimization performance of differential evolution algorithm, by studying the implementation mechanism of differential evolution algorithm, a new idea of incorporating differential strategy and rotation of qubits in the Bloch sphere is proposed in this paper. In the proposed approach, the individuals are encoded by qubits described on Bloch sphere, and the rotation angles of qubits in current individual are obtained by differential strategy. The axis of rotation is designed by using vector product theory, and the rotation matrixes are constructed by using Pauli matrixes. Taking the corresponding qubits in current best individual as targets, the qubits in current individual are rotated to the target qubits about the rotation axis on the Bloch sphere. The Hadamard gates are used to mutate individuals. The simulation results of optimizing the minimum value of functions indicate that, for an iterative step, the average time of the proposed approach is 13 times as long as that of the classical differential evolution algorithm. When the same limited steps are applied in two approaches, the average optimization result of the proposed approach is 0.3 times as great as that of the classical differential evolution algorithm; when the same running time is applied in two approaches, the average optimization result of the proposed approach is 0.4 times as great as that of the classical differential evolution algorithm. These results suggest that the proposed approach is inefficient in computational ability; however, it is obviously efficient in optimization ability, and the overall optimization performance is better than that of the classical differential evolution algorithm.

Investigating the run-time searching behavior of the differential evolution algorithm applied to water distribution system optimization

In recent years, the differential evolution algorithm (DEA) has frequently been used to tackle various water resource problems due to its powerful search ability. However, one challenge of using the DEA is the tedious effort required to fine-tune parameter values due to a lack of theoretical understanding of what governs its searching behavior. This study investigates DEA's search behavior as a function of its parameter values. A range of behavioral metrics are developed to measure run-time statistics about DEA's performance, with primary focus on the search quality, convergence properties and solution generation statistics. Water distribution system design problems are utilized to enable investigation of the behavioral analysis using the developed metrics. Results obtained offer an improved knowledge on how the control parameter values affect DEA's search behavior, thereby providing guidance for parameter-tuning and hence hopefully increasing appropriate take-up of the DEA within the industry in tackling water resource optimization problems.

An Improved Differential Evolution Algorithm Based on Adaptive Parameter

The differential evolution (DE) algorithm is a heuristic global optimization technique based on population which is easy to understand, simple to implement, reliable, and fast. The evolutionary parameters directly influence the performance of differential evolution algorithm. The adjustment of control parameters is a global behavior and has no general research theory to control the parameters in the evolution process at present. In this paper, we propose an adaptive parameter adjustment method which can dynamically adjust control parameters according to the evolution stage. The experiments on high dimensional function optimization showed that the improved algorithm has more powerful global exploration ability and faster convergence speed.

Improving the performance of differential evolution algorithm using Cauchy mutation

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison with basic DE and several other contemporary optimization algorithms.